Lawrence C. Evans Delivers 2011 Porcelli Lectures

The 2011 Porcelli Lectures speaker is Professor Lawrence C. Evans of University of California, Berkeley.

Lectures

Linearity and linearization

Tuesday, March 22, 2011, 3:40–4:30

This expository lecture, aimed at a general audience, will first discuss the profound
advantages of linear structure in mathematical problems and then survey several interesting
ways to “linearize” nonlinear problems, primarily differential equations.
Examples and applications will include perturbation and implicit function procedures,
blow-up techniques, kinetic formulations, and adjoint methods based upon
formal linearization.

Convexity as one-sided linearity

Wednesday, March 23, 2011, 3:40–4:30

This second lecture will continue the themes of the previous talk, surveying for differential
equations various convexity methods that can be interpreted as “one-sided
linearity” tricks. These are especially useful since, as it will be shown, several important
and highly nonlinear problems possess “hidden” convex structures of various
sorts.

Linear adjoint methods for sup-norm variational problems

Thursday, March 24, 2011, 3:40–4:30

The final lecture will present some technical details about a recent application of
linearization and adjoint methods for proving differentiability for weak solutions of
the so-called “infinity Laplacian” PDE. This highly degenerate and nonlinear equation
is fundamental in the emerging field of sup-norm variational problems and their
applications.

Lawrence C. Evans

Lawrence C. Evans, a Professor of Mathematics at the University of California, Berkeley, is a leading expert on nonlinear differential equations, author of over one hundred research papers, and of three books, including the classic graduate textbook “Partial Differential Equations”. In 2004, Professor Evans, jointly with Nikolai V. Krylov, received the prestigious Leroy P. Steele Prize for Seminal Contribution to Research.